Existence of solutions for -order nonlinear -Laplacian differential equations

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• 作者：Lorena Saavedra^a ; ^{lorena.saavedra@usc.es" class="auth_mail" title="E-mail the corresponding author} ; Stepan Tersian^b ; ¹ ; ^{sterzian@uni-ruse.bg" class="auth_mail" title="E-mail the corresponding author}
• 关键词：pp-Laplacian ; Clark&rsquo ; s theorem ; Periodic boundary value problem
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：34
• 期：Complete
• 页码：507-519
• 全文大小：646 K

文摘

The aim of this paper is to study the existence and multiplicity of weak and classic solutions for a class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816301213&_mathId=si1.gif&_user=111111111&_pii=S1468121816301213&_rdoc=1&_issn=14681218&md5=cb4e719486cf5d2f6717f0de831fd2c8">class="imgLazyJSB inlineImage" height="9" width="30" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S1468121816301213-si1.gif">class="mathContainer hidden">class="mathCode">$2n\mathrm{th}$-order differential equation involving the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S1468121816301213&_mathId=si2.gif&_user=111111111&_pii=S1468121816301213&_rdoc=1&_issn=14681218&md5=feeb14e0dc4b701e05eb2233d18ae0b5" title="Click to view the MathML source">pclass="mathContainer hidden">class="mathCode">$p$-Laplacian coupled with periodic boundary conditions. The results are proved by using the minimization argument and an extended Clark’s theorem. Some particular cases are shown.